This article deals with the buckling analysis of perfectly bonded cross-ply laminated composite plates reinforced by wavy carbon nanotubes (CNTs) under in-plane loads using element free Galerkin (EFG) method based on first-order shear deformation theory (FSDT). The wavy single-walled CNTs and Poly-co-vinylene are used for the fibers and the matrix, respectively. The CNT fibers are distributed in the polymer matrix in four types of arrangements in each layer. The material properties of the laminated nanocomposite plates are estimated through a micromechanical model based on the extended rule of mixture. The minimum potential energy approach is utilized to obtain the governing equations and the stiffness matrices. Full transformation approach is employed to enforce essential boundary conditions. The accuracy and convergency of the EFG method is established by comparing the obtained results with available literature. Then, the effects of CNT volume fraction and waviness, aspect ratio and distribution type of CNTs as well as plate aspect ratio, plate width-to-thickness ratio and boundary conditions on the buckling behaviour of cross-ply laminated functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates are investigated. The numerical results show that the CNT waviness and aspect ratio have significant effects on the buckling behaviour of FG-CNTRC plates.